Herbivores play an important role in determining the structure and function of tropical savannahs. Here, we (i) outline a framework for how interactions among large mammalian herbivores, carnivores and environmental variation influence herbivore habitat occupancy in tropical savannahs. We then (ii) use a Bayesian hierarchical model to analyse camera trap data to quantify spatial patterns of habitat occupancy for lions and eight common ungulates of varying body size across an approximately 1100 km 2 landscape in the Serengeti ecosystem. Our results reveal strong positive associations among herbivores at the scale of the entire landscape. Lions were positively associated with migratory ungulates but negatively associated with residents. Herbivore habitat occupancy differed with body size and migratory strategy: large-bodied migrants, at less risk of predation and able to tolerate lower quality food, were associated with high NDVI, while smaller residents, constrained to higher quality forage, avoided these areas. Small herbivores were strongly associated with fires, likely due to the subsequent high-quality regrowth, while larger herbivores avoided burned areas. Body mass was strongly related to herbivore habitat use, with larger species more strongly associated with riverine and woodlands than smaller species. Large-bodied migrants displayed diffuse habitat occupancy, whereas smaller species demonstrated fine-scale occupancy reflecting use of smaller patches of high-quality habitat. Our results demonstrate the emergence of strong positive spatial associations among a diverse group of savannah herbivores, while highlighting species-specific habitat selection strongly determined by herbivore body size. This article is part of the themed issue 'Tropical grassy biomes: linking ecology, human use and conservation'.

Abstract. The Somos-5 sequence is defined by a 0 = a 1 = a 2 = a 3 = a 4 = 1 and a m = for m ≥ 5. We relate the arithmetic of the Somos-5 sequence to the elliptic curve E : y 2 + xy = x 3 + x 2 − 2x and use properties of Galois representations attached to E to prove the density of primes p dividing some term in the Somos-5 sequence is equal to 5087 10752.

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The published literature does not provide a consensus regarding maximum body sizes of North America's largest wild freshwater turtles (genus Macrochelys). The largest known wild M. suwanniensis (Suwannee Alligator Snapping Turtle) currently exists as a curated specimen measuring 713 mm straight-midline carapace length, 801 mm maximum carapace length, 619 mm maximum carapace width, and 236 mm maximum head width. The turtle was never weighed, but we used morphometric data from our studies in the Santa Fe and Suwannee rivers to estimate that it weighed ∼76.4 kg (168 lbs) when captured. Our 95% prediction interval (67.6–86.3 kg [149–190 lbs]) suggests that speculative estimates and anecdotal reports of M. suwanniensis that weigh ≥90 kg (≥200 lbs) are dubious.